Couldn't it just be a case of expansion, or also to limit confusion?
Perhaps when Starfleet began there were only a few fleets that had different insignias, like the modern Navy, each ship has a designated seal design, (as also reflected in ST:Enterprise). Also, each space shuttle mission has a specific logo, perhaps these influenced starfleet insignias. Not just fleet but mission, or even sector of space each ship was assigned got it's own insignia. But then at some point with all the fleets of ships and missions, and meeting so many new cultures and new civilizations they opted to unify Starfleet under one symbol, and it happened to be the delta shield, no other reason, perhaps a vote was taken. Just to limit confusion among all the first contact situations. And other interactions with known races and planets.